Improved unmanned aerial vehicle three-dimensional path planning research method based on HO algorithm

Abstract

The invention discloses an improved unmanned aerial vehicle three-dimensional path planning research method based on a HO algorithm, and aims to solve the problems that the expression of a traditional Hipppous Optimization Algorithm (HOA) in a path space is not visual, local optimum is easily caused, and the convergence speed is relatively low. According to the method, firstly, a spherical vector principle is introduced, the size, the elevation angle and the azimuth angle are mapped into the path length, the turning angle and the climbing angle of the unmanned aerial vehicle, the corresponding relation between path parameters and space coordinates is achieved, and the path smoothness is improved; secondly, introducing an escape factor in a defense stage, and dynamically adjusting the position of an individual to enhance the capability of jumping out of local optimum; and finally, combining a differential evolution mechanism in an escape stage, and carrying out weighted fusion on the differential variation solution and the candidate solution, so that the search diversity and convergence efficiency are improved. According to the method, efficient path searching of the unmanned aerial vehicle in the three-dimensional space can be achieved in the complex environment, the experimental result shows that the generated path is smoother and lower in fitness, and the effectiveness and practicability of unmanned aerial vehicle path planning are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to a research method for three-dimensional path planning of an unmanned aerial vehicle based on an improved HO algorithm, and belongs to the technical field of path planning and optimization of unmanned aerial vehicles. TECHNICAL BACKGROUND

[0002] Unmanned aerial vehicle path planning is a key technology in unmanned aerial vehicle task execution, which aims to find the optimal or suboptimal path for the unmanned aerial vehicle from the starting point to the target point in a complex environment, while avoiding obstacles and meeting fuel, time and safety constraints. Traditional path planning methods, such as A* algorithm and Dijkstra algorithm, although perform well in simple scenarios, often face problems such as large amount of calculation, easy to fall into local optimum, insufficient real-time performance, etc. in dynamic and complex environments, which is difficult to meet the efficiency and robustness requirements of modern unmanned aerial vehicle tasks. In order to solve these limitations, in recent years, heuristic optimization algorithms have gradually become a research hotspot. This kind of algorithm can find global optimal solution in complex search space by simulating natural phenomena or biological behavior, and has strong adaptability and robustness. Among them, Hippopotamus Optimization Algorithm (HOA) as a new heuristic algorithm, inspired by the social behavior of hippopotamus, such as territory consciousness and group cooperation, builds a mathematical model by simulating these behaviors, showing strong global search ability, fast convergence speed and simple parameter setting, etc. It is particularly suitable for solving complex optimization problems. Applying Hippopotamus Optimization Algorithm (HOA) to unmanned aerial vehicle path planning can effectively improve the path search efficiency, quickly generate optimal path in dynamic environment, avoid moving obstacles, and support multi-objective optimization requirements, such as optimizing path length, energy consumption and task completion time at the same time. In addition, the parallel search mechanism of Hippopotamus Optimization Algorithm (HOA) enables it to handle large-scale, high-dimensional path planning problems, providing a new solution for the application of unmanned aerial vehicles in complex scenarios. This research not only has important theoretical value, but also provides technical support for the practical application of unmanned aerial vehicles in military reconnaissance, disaster monitoring, logistics distribution and other fields, and has broad application prospects. However, the path planning based on Hippopotamus Optimization Algorithm (HOA) still faces some challenges, such as algorithm parameter tuning, dynamic environment adaptability and integration with other intelligent technologies, etc. Future research needs to further optimize the algorithm performance and combine machine learning, deep learning and other methods to improve the intelligent level of path planning to meet more complex and variable task requirements. SUMMARY

[0003] The purpose of the present application is to provide a research method for three-dimensional path planning of unmanned aerial vehicles based on improved HO algorithm, so as to solve the problem of safe flight path planning of unmanned aerial vehicles in complex environment. The Hippopotamus Optimization Algorithm (HOA) is improved by introducing the principle of spherical vector. The size, elevation and azimuth of the spherical vector are mapped to the path length, turning angle and climbing angle of the unmanned aerial vehicle respectively, so as to establish the mutual relationship between them and the spatial position coordinates. In the defense stage of the Hippopotamus Optimization Algorithm, an escape factor is introduced to reselect and update the position. In the escape stage, the position generated by the difference mutation mechanism is combined with the position selected in the escape stage by weighted fusion, so as to obtain a new position. The present application effectively solves the problem of slow convergence speed and easy to fall into local optimal solution of the traditional Hippopotamus Optimization Algorithm (HOA). By using the path planning method based on improved HO algorithm for path search in three-dimensional space of unmanned aerial vehicles, the generated path is smoother, the fitness is lower, and the effectiveness and practicability of the path are significantly improved.

[0004] The technical solution adopted by the present application to solve its technical problems is: a research method for three-dimensional path planning of unmanned aerial vehicles based on improved HO algorithm, comprising the following steps:

[0005] Step 1: based on digital elevation model to construct three-dimensional terrain environment and set obstacle constraints, establish spatial modeling framework; on this basis, set constraint conditions such as path length, flight height, obstacle avoidance and path smoothness, and quantify through target cost function, to provide support for safe flight path planning of unmanned aerial vehicles in complex environment.

[0006] Step 2: in this stage, Hippopotamus population is randomly generated and its position is initialized. In view of the problem of insufficient population diversity and non-intuitive path expression in the traditional initialization stage, an initialization method based on spherical vector mapping is proposed. Each unmanned aerial vehicle path is represented as a series of vectors using spherical coordinate system, in which the size, elevation and azimuth of the vector are mapped to the path length, turning angle and climbing angle respectively. This improvement not only enhances the geometric intuitiveness and controllability of path representation, but also effectively improves the diversity and search quality of the initial population.

[0007] Step 3: In this stage, the improved hippo optimization algorithm is used to perform global search in three-dimensional space. In view of the problems that the traditional hippo optimization algorithm is easy to fall into local optimum in the search process, and the balance between global exploration and local development is insufficient, the adaptive weight factor mechanism is introduced, the proportion of exploration and development is dynamically adjusted according to the iteration process, and the diversified update of candidate solutions is realized by combining the escape factor and the differential evolution strategy. The improvement effectively enhances the global search ability and the ability to jump out of the local optimum, so as to quickly obtain a better solution set and improve the convergence efficiency and robustness of path planning.

[0008] Step 4: Finally output a set of optimal path solution set to provide a safe and reliable flight path for the unmanned aerial vehicle in a complex environment.

[0009] Further, the step 1 of the present application builds the environment required for unmanned aerial vehicle path planning, including:

[0010] Firstly, a three-dimensional terrain scene is established based on a digital elevation map model, and reasonable spatial range and height boundary conditions are set;

[0011] In terms of obstacle design, multiple scenes with different complexity levels are constructed, and the progressive characteristics of environmental complexity are embodied by gradually increasing the number and distribution density of obstacles;

[0012] In the flight task configuration, the starting point and target point of the unmanned aerial vehicle are set, and several key waypoints are added in the flight path to ensure that the path planning task is representative and challenging.

[0013] Further, the constraint conditions and target cost function of the unmanned aerial vehicle path planning designed by the present application include:

[0014] When the unmanned aerial vehicle flies through n waypoints, X i represents, then each path point coordinate is P ij =(x ij ,y ij ,z ij ), and the specific expression of the target cost function F1 is:

[0015]

[0016] Wherein, F1(X i ) represents the target function value.

[0017]

[0018] Wherein, d(P ij , P i，j+1 ) represents the distance between P ij and P i，j+1 , x ij and x i，j+1P ij and P i，j+1 Position of x-axis on two points, y ij and y i,j+1 P ij and P i，j+1 Position of x-axis on two points, z ij and z i，j+1 P ij and P i，j+1 Position of x-axis on two points.

[0019] Set the minimum and maximum flight height as h min and h max′ Then the height cost related to waypoint P ij can be calculated by the following formula:

[0020]

[0021] Where H ij is the height cost function value, h ij is the flight height on waypoint P ij , h min and h max are the minimum and maximum flight height respectively, and the cost function values H ij of all waypoints are summed up to get the total height cost F2, which is expressed as:

[0022]

[0023] Where F2(X i ) is the total height cost function value, and H ij is the height cost function value of the waypoint.

[0024] Let T represent the set of all obstacles, where the center coordinates of each obstacle are C t , and the influence area of the obstacle is divided into the following three parts: the high-threat area (inner ring) includes buildings, high-voltage power lines, and other non-crossable obstacles, with a radius of R t , which must be strictly avoided by the UAV, otherwise a very high cost will be generated, the middle ring corresponds to the edge of the flight restricted area and also takes into account the diameter of the UAV, with a ring width of K t , flying in this area will also increase the flight risk; the low-threat area (outer ring) corresponds to the air traffic dense area, with a ring width of M t , although it will not directly lead to collision risk, but may affect the flight stability, and its threat cost is proportional to the distance d t from C t ; the safe area is located outside all threat areas and will not generate additional cost to the UAV's path. Assuming a certain path from waypoint P ijTo P i，j+1 , the vertical distance of the path to the center point of the obstacle is d t , the path cost F3 can be expressed as:

[0025]

[0026] Where F3 represents the total path cost, R t is the radius of the high-threat area, K t is the intermediate ring width, the vertical distance of the path to the center point of the obstacle is d t , M t is the low-threat area ring width.

[0027] Let the three consecutive waypoints on the path be P i，j-1 , P ij and P i，j+1 , the turning angle is the angle formed by the projection of the two paths on the horizontal plane, and the projection vector is specifically expressed as:

[0028]

[0029] Where, represents the projection vector of P ij and P i，j+1 , represents the vertical direction vector, represents the vector of P ij and P i，j+1 , P i，j-1 , P ij and P i，j+1 represent the three waypoints respectively.

[0030] The turning angle is specifically expressed as:

[0031]

[0032] Where, represents the turning angle, is the projection vector corresponding to P ij and P i，j+1 , is the projection vector corresponding to P i，j+1 and P i，j+2 .

[0033] The climb angle ψ ij is the angle between the path segment and its projection on the horizontal plane, and its specific expression is:

[0034]

[0035] wherein ψ ij represents the climb angle, z i，j+1 and z ij are the positions of the waypoint in the z-axis direction.

[0036] The specific expression of the smoothing cost F4 is as follows:

[0037]

[0038] wherein F4(X i ) represents the value of the smoothing cost function, ψ ij represents the climb angle.

[0039] In consideration of multiple influencing factors, a total cost function is constructed, which is the weighted cumulative sum of the cost functions under various constraint conditions, and the specific expression is as follows:

[0040]

[0041] wherein F4(X i ) represents the value of the smoothing cost function, ψ represents the turn angle, a1 represents the weight of the turn angle, ψ ij represents the climb angle, a2 represents the weight of the climb angle, ψ i，j-1 represents the climb angle of the previous position. ij The specific expression of the total cost function is as follows:

[0042] Further, the path is expressed as a series of vectors in the step 2 of the present application, expressed in the spherical coordinate system, and finally mapped into the rectangular coordinate, which comprises:

[0043] The vector is expressed in the spherical coordinate system, which comprises three key parameters: the length of the adjacent path point ρ∈(0, the path length), the flight elevation angle and the flight azimuth angle For a flight path Ω i with N nodes, it can be expressed as a 3N-dimensional hyperspherical vector:

[0044]

[0045] wherein Ω i represents the flight path set, ρ represents the length of the adjacent path point, ψ represents the flight elevation angle, and represents the flight azimuth angle.

[0046] The spherical vector is recorded as u ij , and is further defined as a vector in the path set Ω i , that is, In order to convert the spherical vector into specific waypoint coordinates P ij= (x ij , y ij , z ij ) ∈ X i , which can be mapped by the following formula, the specific expression is:

[0047]

[0048] z ij = z i，j-1 + ρ ij cosψ ij , (14)

[0049] Wherein, x ij and x i，j-1 represent the position of the x-axis on P ij and P i，j-1 , y ij and y i,j-1 represent the position of the x-axis on P ij and P i，j-1 , z ij and z i，j-1 represent the position of the x-axis on P ij and P i，j-1 , ρ represents the length of adjacent path point, ψ represents the flight elevation angle, represent the flight azimuth angle.

[0050] Further, the three-dimensional path planning research method of the unmanned aerial vehicle based on the HO algorithm improvement provided by the present application comprises:

[0051] Method comprises:

[0052] Each hippo represents the position in space, the position of the hippo population is randomly generated in the initialization stage, which can be represented by the following formula:

[0053] X i : x ij = 1 j + r·(u j -l j ), (15)

[0054] Wherein, X i represents the position of the ith candidate solution, r is a random number between 0 and 1, l and u respectively represent the lower bound and upper bound of the jth decision variable. N represents the population size of the hippo population, n represents the number of decision variables in the problem, then the hippo population matrix has the following specific expression:

[0055]

[0056] Wherein, X is the hippo population matrix, X i represents the ith candidate hippo position.

[0057] The whole process of Hippopotamus Optimization Algorithm (HOA) can be divided into three stages: position updating, defense, and escape. The specific algorithm is described as follows:

[0058] First stage: position updating stage (exploration stage)

[0059] The hippo population is composed of several adult female hippos, baby hippos, multiple adult male hippos, and a dominant male hippo (the leader of the group). In the optimization algorithm, the position of the dominant male hippo needs to be updated constantly through iterative calculation to ensure that the cost function reaches the minimum value. Formula (17) describes the position updating mechanism of male hippos in lakes or ponds, simulating the mathematical model of their search for the optimal position in the environment.

[0060]

[0061] wherein, represents the position of the male hippo, x D represents the position of the dominant hippo (the hippo with the smallest cost function value in the current iteration). is a random vector between 0 and 1, is a random number between 0 and 1 (see formula (18)), and I1 and I2 are integers between 1 and 2 (see formulas (17) and (18)). MG i refers to the mean of some randomly selected hippos, which have equal probability of containing the hippo X i under consideration, y1 is a random number between 0 and 1 (see formula (17)). In formula (18), Q1 and Q2 are integer random numbers, which can be 1 or 0.

[0062]

[0063] wherein, I1 and I2 are integers between 1 and 2, is a random vector between 0 and 1, is a random number between 0 and 1, and Q1 and Q2 are integer random numbers, which can be 1 or 0.

[0064]

[0065] The position of a female or immature hippo in the group The specific expression is:

[0066]

[0067] wherein, the specific expression of R is:

[0068]

[0069] where r6 and r7 are a number between 0 and 1 (see equation (21)), hi and h2 are randomly selected values or vectors from the five scenarios in equation (18).

[0070] The position update of the male and female or immature hippo in the group is given by:

[0071]

[0072] where F i is the cost function value, is the position of the male hippo, is the position of the female or immature hippo.

[0073] Second stage: defense stage

[0074] The hippo group will take action to resist the threat of the predator. The position of the predator in space is given by:

[0075]

[0076] where Pd j represents the position of the predator, represents a random vector, each element of the vector has a value between 0 and 1, and l and u represent the lower and upper bounds of the jth decision variable, respectively.

[0077] The distance between the ith hippo and the predator is:

[0078]

[0079] where, is the distance between the predator and the hippo, Pd j represents the position of the predator, and x ij represents the position of the hippo.

[0080] Through the study of the second stage of the hippo optimization algorithm, it is found that the hippo takes appropriate defense strategies according to the size of to protect itself from the threat of the predator. When is less than Fi, it means that the predator is very close, at which time the hippo will quickly adjust the direction and actively move towards the predator to exert pressure to force it to retreat. When is larger, it indicates that the predator or invader is still in a distant position, at which time the hippo does not need to take immediate action, but remains vigilant and observes the other party's movements, and does not make drastic changes. However, it should be noted that when is less than F iWhen the hippo directly moves towards the predator, it may bring unnecessary danger, especially in complex environments, and too close to the predator may expose the hippo to more threats. Therefore, the hippo optimization algorithm is proposed by introducing an escape factor based on the spherical vector coordinates. When calculating the updated position, the escape factor can be combined with the updated path position to adjust the movement direction of the hippo, produce a certain degree of fluctuation in the short term, avoid falling into the local optimal solution, and finally find a better global solution. The specific expressions of the escape factor and the position of the hippo when facing the predator are as follows:

[0081]

[0082] where, , j = 1, 2, …, n. is a random vector subject to the Levy distribution, which is used to simulate the mutation of the position when the predator attacks the hippo. In equation (27), f is a uniform random number between 2 and 4, c is a uniform random number between 1 and 1.5, and d is a uniform random number between 2 and 3. g is a uniform random number between -1 and 1. is a random vector of dimension 1 x m. The mathematical model of Levy motion is specifically expressed as:

[0083]

[0084] where ω and υ are random numbers in the interval [0, 1], θ is a constant equal to 1.5, Γ is the abbreviation of the gamma function, and σ ω can be calculated by equation (29).

[0085]

[0086] where θ is a constant equal to 1.5, r is the abbreviation of the gamma function,

[0087] The hippo position updated in this stage is represented as:

[0088]

[0089] where, the new defensive position to be found, the cost function value of the new defensive position.

[0090] Third stage: escape stage (development stage)

[0091] According to the modeling of the hippo's behavior when escaping from the predator, the following is obtained:

[0092]

[0093] where t denotes the current iteration number, and T denotes the maximum iteration number MaxIter. denotes the position of the hippo that is closest to the safe position. a1 is a random vector or number that is randomly selected from three scenarios a in equation (33), denotes a random vector between 0 and 1, while r 12 and r 13 denote random numbers generated in the range of 0 and 1. In addition, r 12 is a normally distributed random number.

[0094] This stage simulates the behavior of the hippo population escaping from the predator, which helps to enhance the exploration ability in local search, but ignores the global search. To make up for this deficiency, the differential evolution algorithm is introduced on the basis of the original algorithm. The differential evolution algorithm generates new individuals by the difference between three random individuals in the current population through the difference mutation mechanism. This mechanism can guide the search process to explore the more superior area, avoiding the algorithm falling into the local optimal solution in the early stage. Therefore, after introducing the differential evolution algorithm, the algorithm can effectively explore the solution space in the global range, so as to find the potential global optimal solution more likely.

[0095] In the improved version, the scaling factor F and the crossover probability CR of the differential evolution are dynamically adjusted with the change of the iteration number, and the specific expressions are as follows:

[0096] F = 0.9 - 0.7 × (t ÷ T), (34)

[0097] CR = 0.1 + 0.8 × (t ÷ T), (35)

[0098] where F denotes the scaling factor, t is the current iteration number, T is the maximum iteration number, and CR denotes the crossover probability.

[0099] The differential evolution body expression is as follows:

[0100] V i = X r1 +F·(X r2 -X r3 ), (36)

[0101]

[0102] where V i is the mutated individual, X r1 , X r2 , and x r3Randomly selected from the population, F is the scaling factor of differential variation, usually set in the range of [0, 1]. Then the path points generated by differential evolution (see formula (36)) and the path points selected by the escape stage of the Hippopotamus Optimization Algorithm (see formula (32)) are weighted and fused, and the results of the two are proportionally adjusted and added to obtain a new path point, and the formula is:

[0103]

[0104] Wherein, W DE = 0.4, W LS = 0.6, for each updated population Calculate its cost function value, if the new cost function value is better, update the position of the population, expressed as formula:

[0105]

[0106] Further, step 4 passes through the maximum number of iterations to find a group of optimal solutions:

[0107] The specific expression of the best position and the target cost function value obtained each time is:

[0108] X ibest =X i , (40)

[0109] F best =F ibest (X ibest ), (41)

[0110] Wherein, X ibest represents the best position, F best represents the optimal cost function value.

[0111] The iteration is terminated, and the global best fitness value is obtained, and the optimal solution is saved.

[0112] Beneficial effects:

[0113] 1、The Hippopotamus Optimization Algorithm (HOA) is improved in the application, the size, elevation and azimuth of the spherical vector are mapped into the path length, turning angle and climbing angle of the unmanned aerial vehicle respectively by introducing the principle of the spherical vector, so that the mutual relationship between the space position coordinates is established, an escape factor is introduced in the defense stage of the Hippopotamus Optimization Algorithm (HOA) to reselect and update the position, and in the escape stage, the position generated by the differential variation mechanism is combined with the position selected in the escape stage, and the positions are weighted and fused, so that a new position is obtained.

[0114] 2、The application effectively solves the problems of slow convergence speed and easy falling into local optimal solution of the hippopotamus optimization algorithm (HOA). The improved HOA-based three-dimensional path planning research method for unmanned aerial vehicles is used for path search in the three-dimensional space of the unmanned aerial vehicles, the generated path is smoother, the fitness is lower, and the effectiveness and practicality of the path are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0115] Figure 1 The method flowchart of the application.

[0116] Figure 2 The unmanned aerial vehicle path overhead view under four complexities.

[0117] Figure 3 The cost function curve diagram obtained by iterating the optimal path of the unmanned aerial vehicle under four complexities. DETAILED DESCRIPTION

[0118] The application will be further described in detail below in combination with the drawings and specific embodiments.

[0119] In the experiment, a digital elevation map model is selected to set the size of the terrain to 450*450 and the height to 400; four selectable complexities are set, the complexity increases successively, and the number of obstacles is 3, 4, 5, and 7 respectively; the starting point (10, 10, 200) and the ending point (400, 400, 150) of the unmanned aerial vehicle flight and the number of 12 waypoints (including the starting point and the ending point) are set;

[0120] Step 1: Select the terrain map and initialize the conditions

[0121] Step 1.1: Select the digital elevation map model, set the size of the terrain to 450*450 and the height to 400;

[0122] Step 1.2: Set four selectable complexities, the complexity increases successively, and the number of obstacles is 3, 4, 5, and 7 respectively;

[0123] Step 1.3: Set the starting point (10, 10, 200) and the ending point (400, 400, 150) of the unmanned aerial vehicle flight and the number of 12 waypoints (including the starting point and the ending point);

[0124] Step 2: Design the constraint conditions and the target cost function of the unmanned aerial vehicle path planning

[0125] Step 2.1.1: Design the path length cost function

[0126] When the unmanned aerial vehicle flies through n waypoints, Xi If the path is represented, then each path point coordinate is P ij = (x ij , y ij , z ij ), and the objective cost function F1 is specifically expressed as:

[0127]

[0128] where F1(X i ) represents the objective function value.

[0129]

[0130] where d(P ij , P i，j+1 ) represents the distance between P ij and P i，j+1 , x ij and x i，j+1 represent the position of the x-axis at P ij and P i，j+1 , y ij and y i，j+1 represent the position of the x-axis at P ij and P i，j+1 , and z ij and z i，j+1 represent the position of the x-axis at P ij and P i，j+1 .

[0131] Step 2.1.2: Design the flight height cost function

[0132] Set the minimum and maximum flight heights as h min and h max , respectively, and the height cost related to the waypoint P ij can be calculated by the following formula:

[0133]

[0134] where H ij is the height cost function value, h ij represents the flight height at the waypoint P ij , h min and h max represent the minimum and maximum flight heights, respectively, and the cost function values H ij of all waypoints are summed to obtain the total height cost F2, which is specifically expressed as:

[0135]

[0136] where F2(X i) represents the total height cost function value, H ij represents the waypoint height cost function value.

[0137] Step 2.1.3: Design the obstacle cost function encountered during flight

[0138] Let T represent the set of all obstacles, where the center coordinates of each obstacle are C t , and the influence area of the obstacle is divided into the following three parts: the high-threat area (inner ring) includes buildings, high-voltage lines, and other non-crossable obstacles, with a radius of R t , which the UAV must strictly avoid, otherwise a very high cost will be generated; the middle ring corresponds to the edge of the flight restricted area and also takes into account the diameter of the UAV, with a ring width of K t , flight in this area will also increase the risk of flight; the low-threat area (outer ring) corresponds to the air traffic dense area, with a ring width of M t , although it will not directly cause collision risk, but may affect the flight stability, its threat cost is proportional to the distance d t from C t ; the safe area is located outside all threat areas and will not generate additional cost to the UAV's path. Assuming a certain path from waypoint P ij to P i，j+1 , the vertical distance of this path to the center point of the obstacle is d t , then the path cost F3 can be represented as:

[0139]

[0140] where F3 represents the total path cost, R t is the radius of the high-threat area, K t is the width of the middle ring, d t is the vertical distance of the path to the center point of the obstacle, and M t is the ring width of the low-threat area.

[0141] Step 2.14: Design the flight turn angle and climb angle smoothing cost function

[0142] Let the three consecutive waypoints on the path be P i，j-1 , P ij , P i，j+1 , the turn angle is the angle formed by the projection of the two paths in the horizontal plane, and the projection vector is specifically expressed as:

[0143]

[0144] where represents the projection vector of P ij and P i，j+1 , Represents the vertical direction vector. P represents ij and P i，j+1 A vector between two points, P i，j-1 P ij and P i，j+1 These represent three waypoints.

[0145] Turning corner The specific expression is:

[0146]

[0147] in, Indicates the turning angle. For P ij and P i，j+1 The projection vectors corresponding to the two points, For P i，j+1 and P i，j+2 The projection vectors corresponding to the two points.

[0148] Ascent angle ψ ij It is a path segment Its projection on the horizontal plane The angle between them is expressed as follows:

[0149]

[0150] Where, ψ ij Indicates the climb angle, z i，j+1 and z ij It is the position of the waypoint along the z-axis.

[0151] The specific expression for the smoothing cost F4 is:

[0152]

[0153] Among them, F4(X) i ) represents the value of the smoothing cost function. Let a1 represent the turning angle and ψ represent the weight of the turning angle. ij a2 represents the climb angle, a2 represents the climb angle weight, and ψ i，j-1 Represents ψ ij The climb angle at the previous position.

[0154] Step 2.2: Design the overall cost function

[0155] Taking into account multiple influencing factors, a total cost function is constructed. This function is a weighted sum of the cost functions under various constraints, and its specific expression is as follows:

[0156]

[0157] Wherein, F(X) i ) represents the total cost function value, a k F represents the weight of the k-th route cost. k (X i ) represents the cost of the k-th route.

[0158] Step 3 represents the path as a series of vectors, using a spherical coordinate system and mapping it to rectangular coordinates.

[0159] The vector is represented in a spherical coordinate system and includes three key parameters: the length of adjacent path points ρ∈(0, path length), and the flight elevation angle. and flight azimuth For a flight path Ω with N nodes i It can be represented as a 3N-dimensional hyperspherical vector:

[0160]

[0161] Among them, Ω i Let ρ represent the set of flight paths, ρ represent the length of adjacent path points, and ψ represent the flight elevation angle. Indicates the flight azimuth angle.

[0162] spherical vector Noted as u ij And further define it as the path set Ω i One of the vectors, namely To convert this spherical vector into specific waypoint coordinates P ij =(x ij y ij , z ij )∈X i The mapping can be performed using the following formula, the specific expression of which is:

[0163]

[0164] z ij =z i，j-1 +ρ ij cosψ ij ,

[0165] Where, x ij and x i，j-1 P represents ij and P i，j-1 The position of two points on the x-axis, y ij and y i，j-1 P represents ij and P i，j-1 The position of two points on the x-axis, z-axis ij and z i，j-1 P representsij and P i，j-1 The position of the two points on the x-axis, p represents the length of the adjacent path point, and ψ represents the flight elevation angle, represents the flight azimuth angle.

[0166] Step 4 uses the improved UAV three-dimensional path planning research method based on the HO algorithm, wherein the flow of the improved HO algorithm is as shown in Figure 1 The specific steps are as follows:

[0167] Step 4.1: Initialize the population. The number of the population is preset to N, and the dimension of the population is n, which constitutes an Nxn search space. Each hippo represents a position in space. In the initialization stage, the positions of the hippo population are randomly generated, which can be represented by the following formula:

[0168] X i : x ij =l j +r·(u j -l j ),

[0169] wherein X i represents the position of the i-th candidate solution, r is a random number between 0 and 1, l and u respectively represent the lower bound and upper bound of the j-th decision variable. N represents the population size of the hippo population, and n represents the number of decision variables in the problem. Then the hippo population matrix is specifically expressed as:

[0170]

[0171] wherein X is the hippo population matrix, and X i represents the i-th candidate hippo position.

[0172] Step 4.2: First stage: position updating stage (exploration stage)

[0173] The hippo population is composed of several adult female hippos, baby hippos, multiple adult male hippos, and a dominant male hippo (the leader of the population). In the optimization algorithm, the position of the dominant male hippo needs to be updated constantly through iterative calculation to ensure that the cost function reaches the minimum value. Formula (16) describes the position updating mechanism of the male hippo in the lake or pond, simulating the mathematical model of its search for the optimal position in the environment.

[0174]

[0175] wherein, represents the position of the male hippo, and x D represents the position of the dominant hippo (the hippo with the minimum cost function value in the current iteration). is a random vector between 0 and 1, is a random number between 0 and 1 (see equation (17)), and I1and I2are integers between 1 and 2 (see equations (16) and (17)). MG i refers to the mean of some randomly selected Hippo, with equal probability of containing the Hippo X currently under consideration i , and y1is a random number between 0 and 1 (see equation (16)). In equation (17), Q1and Q2are integer random numbers, which can be either 1 or 0.

[0176]

[0177] where I1and I2are integers between 1 and 2, is a random vector between 0 and 1, is a random number between 0 and 1, and Q1and Q2are integer random numbers, which can be either 1 or 0.

[0178]

[0179] the position of a female Hippo or immature Hippo in the herd The specific expression is:

[0180]

[0181] where the specific expression for R is:

[0182]

[0183] where r6and r7are numbers between 0 and 1 (see equation (20)), and h1and h2are values or vectors randomly selected from the five scenarios in equation (17).

[0184] The specific expression for the position update of a male and female or immature Hippo in the herd is:

[0185]

[0186] where F i is the cost function value is the position of a male Hippo, is the position of a female or immature Hippo.

[0187] Step 4.3: Second phase: defense phase

[0188] The Hippo herd will take action to defend against the threat of the predator. The specific expression for the position of the predator in space is:

[0189]

[0190] where Pdj represents the position of the predator, represents a random vector, the value of each element in the vector is between 0 and 1, and l and u represent the lower bound and upper bound of the jth decision variable, respectively.

[0191] The distance between the ith hippo and the predator is:

[0192]

[0193] wherein, is the distance between the predator and the hippo, Pd j represents the position of the predator, x ij represents the position of the hippo.

[0194] Through the study of the second phase of the hippo optimization algorithm, it is found that the hippo takes corresponding defense strategies according to the size of to protect itself from the threat of the predator. When is less than F i , it means that the predator has approached very close, at which time the hippo will quickly adjust the direction and actively move towards the predator to exert pressure to force it to retreat. When is larger, it indicates that the predator or invader is still in a distant position, at which time the hippo does not need to take immediate action, but remains vigilant and observes the other party's movements, and does not make drastic changes. However, it needs to be noted that when is less than F i , the hippo directly moving towards the predator may bring unnecessary danger, especially in complex environments, too close to the predator may expose the hippo to more threats, therefore, the hippo optimization algorithm is proposed by introducing an escape factor based on the spherical vector coordinates, which can combine the escape factor with the updated path position to adjust the movement direction of the hippo, produce a certain degree of fluctuation in the short term, avoid falling into local optimal solution, and finally find a better global solution. The specific expressions of the escape factor and the position of the hippo when facing the predator are:

[0195]

[0196] wherein, , j = 1, 2,..., n. is a random vector subject to Levy distribution, used to simulate the mutation of the position when the predator attacks the hippo. In equation (26), f is a uniform random number between 2 and 4, c is a uniform random number between 1 and 1.5, d is a uniform random number between 2 and 3. g is a uniform random number between -1 and 1. is a random vector of dimension 1 x m. The mathematical model of Levy motion is specifically expressed as:

[0197]

[0198] where ω and υ are random numbers in the interval [0, 1], θ is a constant equal to 1.5, Γ is a shorthand for the gamma function, σ ω This can be calculated by equation (28).

[0199]

[0200] The hippo position updated in this stage is denoted as:

[0201]

[0202] where, The new defensive position sought, is the cost function value of the new defensive position.

[0203] Step 4.4: Third Stage: Escape Stage (Development Stage)

[0204] According to the behavior of the hippo escaping from the predator, it is modeled as follows:

[0205]

[0206] where t represents the current iteration number, and T represents the maximum iteration number MaxIter. represents the position of the hippo seeking the closest safe position. α1 is a random vector or number randomly selected from three scenarios α in equation (32), represents a random vector between 0 and 1, while r 12 and r 13 represent random numbers generated in the range of 0 and 1. In addition, r 12 is a normally distributed random number.

[0207] This stage simulates the behavior of the hippo population escaping from the predator, which helps to enhance the exploration ability in local search, but neglects the global search. To make up for this deficiency, the differential evolution algorithm is introduced based on the original algorithm. The differential evolution algorithm generates new individuals by the difference between three random individuals in the current population. This mechanism can guide the search process to explore more superior areas and avoid falling into local optimal solutions in the early stage. Therefore, after introducing the differential evolution algorithm, the algorithm can effectively explore the solution space in the global range, making it more likely to find potential global optimal solutions.

[0208] In the improved version, the scaling factor F and the crossover probability CR of the differential evolution are dynamically adjusted with the change of the iteration number, and the specific expression is:

[0209] F = 0.9 - 0.7 × (t ÷ T),

[0210] CR = 0.1 + 0.8 × (t ÷ T),

[0211] Where F represents the scaling factor, t is the current iteration number, T is the maximum iteration number, and CR represents the crossover probability.

[0212] The differential evolutionary expression is:

[0213] V i =X r1 +F·(X r2 -X r3 ),

[0214]

[0215] Among them, V i It is a mutated individual, X r1 X r2 X r3 Randomly selected from the population, F is the scaling factor for differential mutation, usually set in the range [0, 1]. Then, the path points generated by differential evolution (see formula (36)) and the path points selected by the escape phase of the hippo optimization algorithm (see formula (31)) are weighted and fused, and the results of the two are added together after proportional adjustment to obtain a new path point, the formula of which is:

[0216]

[0217] Among them, W DE W is 0.4. LS The value is 0.6 for each updated population. Calculate the cost function value. If the new cost function value is better, update the population position, expressed by the formula:

[0218]

[0219] in, This indicates the position selected in this stage. This is the cost function value corresponding to that point.

[0220] Step 5: Repeat steps 3 and 4 until a set of optimal solutions is found after the maximum number of iterations.

[0221] The specific expression for obtaining the optimal position and the target cost function value in each iteration is as follows:

[0222] X ibest =X i ,

[0223] F best =Fibest (X ibest ),

[0224] where X ibest represents the best position, F best represents the best cost function value.

[0225] The iteration is terminated, the global best fitness value is obtained, and the optimal solution is saved.

[0226] Step 6: Repeat the above steps to obtain the result in the different complexity environment, as shown in the top view path diagram Figure 2 , and the cost function curve obtained by iteration is as shown in Figure 3 .

Claims

1. A research method for three-dimensional path planning of a UAV based on an improved HO algorithm, characterized in that, The method comprises the following steps: Step 1: Construct a three-dimensional terrain environment based on a digital elevation model and set obstacle constraints to establish a spatial modeling framework; on this basis, set constraint conditions such as path length, flight height, obstacle avoidance and path smoothness, and quantify through a target cost function to provide support for safe flight path planning of the unmanned aerial vehicle in a complex environment. Step 2: In this stage, a hippo population is randomly generated and initialized. In view of the problems of insufficient population diversity and non-intuitive path expression in the traditional initialization stage, an initialization method based on spherical vector mapping is proposed, in which each unmanned aerial vehicle path is represented as a series of vectors in a spherical coordinate system, and the size, elevation angle and azimuth angle of the vector are mapped to the path length, turning angle and climbing angle respectively. The improvement not only enhances the geometric intuitiveness and controllability of path representation, but also effectively improves the diversity and search quality of the initial population. Step 3: In this stage, the improved hippo optimization algorithm is used to perform global search in three-dimensional space. In view of the problems of the traditional hippo optimization algorithm that is easy to fall into local optimum and the balance between global exploration and local development is insufficient in the search process, an adaptive weight factor mechanism is introduced, the proportion of exploration and development is dynamically adjusted according to the iteration process, and the diversified update of candidate solutions is realized by combining the escape factor and differential evolution strategy. The improvement effectively enhances the global search ability and the ability to jump out of local optimum, so as to quickly obtain a better solution set and improve the convergence efficiency and robustness of path planning. Step 4: Finally, a set of optimal path solutions is output to provide a safe and reliable flight path for the unmanned aerial vehicle in a complex environment.

2. The method of claim 1, wherein the method is improved based on a HO algorithm. The step 1 first builds the environment required for unmanned aerial vehicle path planning, including: First, a three-dimensional terrain scene is established based on a digital elevation map model, and reasonable spatial range and height boundary conditions are set; In terms of obstacle design, multiple scenes with different complexity levels are constructed to reflect the progressive characteristics of environmental complexity by gradually increasing the number and distribution density of obstacles; In the flight task configuration, the starting point and target point of the unmanned aerial vehicle are set, and several key waypoints are added to the flight path to ensure that the path planning task is representative and challenging. The unmanned aerial vehicle three-dimensional path planning research method based on the improved HO algorithm according to claim 1, wherein the step 1 of designing the unmanned aerial vehicle path planning constraint conditions and the target cost function comprises: When the UAV flies through n waypoints, X i is used to represent, then each path point coordinate is P ij = (x ij , y ij , z ij ), and the target cost function F1 is specifically expressed as: where F1(X i ) represents the objective function value. where d(P ij , P i，j+1 ) represents the distance between P ij and P i，j+1 , x ij and x i，j+1 represent the position of P ij and P i，j+1 on the x-axis, y ij and y i，j+1 represent the position of P ij and P i，j+1 on the y-axis, and z ij and z i，j+1 represent the position of P ij and P i，j+1 on the z-axis. The minimum and maximum flight heights are set to h min and h max respectively, then the height cost associated with the waypoint P ij may be calculated by the following equation: where H ij a high altitude cost function value, h ij represents the flight altitude at waypoint P ij h min and h max represent the minimum and maximum flight altitudes, respectively, and the cost function values H ij for all waypoints are summed to obtain the total altitude cost F2, which is given by where F2(X i ) represents the total height cost function value, H ij represents the waypoint height cost function value. Let T represent the set of all obstacles, where each obstacle has a center coordinate C t , the influence area of an obstacle is divided into three parts: the high-threat region (inner ring) includes impassable obstacles such as buildings and high-voltage power lines, with a radius R t , the UAV must strictly avoid, otherwise it will incur a very high cost, the middle ring corresponds to the edge of the flight restricted area and also takes into account the diameter of the UAV, with a ring width K t , flight in this area will also increase the risk of flight; the low-threat region (outer ring) corresponds to the air traffic dense area, with a ring width M t , although it will not directly lead to collision risk, but may affect the flight stability, its threat cost is proportional to its distance d t to C t ; the safe region is located outside all threat regions, and will not incur additional cost to the UAV's path. Assuming a certain path from waypoint P ij to P i，j+1 , the vertical distance of this path to the center point of the obstacle is d t , then the path cost F3 can be represented as: where F3 represents the total path cost, R t is the high-threat zone radius, K t is the intermediate ring width, and d t is the vertical distance of the path to the center point of the obstacle t is the low-threat zone ring width. Let the three consecutive waypoints on the path be P i，j-1 , P ij , and P i，j+1 , and the turning angle be the angle formed by the two paths in the horizontal plane projection, and the projection vector be specifically expressed as: wherein, represents P ij and P i，j+1 the projection vector of two points, represents the perpendicular direction vector, represents P ij and P i，j+1 the vector of two points, P i，j-1 , P ij and P i,j+1 represent three waypoints, respectively. cornering angle The specific expression is: wherein, denotes the turning angle, is P ij and P i，j+1 the projection vector corresponding to the two points, is P i，j+1 and P i，j+2 the projection vector corresponding to the two points. climb angle ψ ij is a path segment with its projection on the horizontal plane the angle between them, which is expressed as: where ψ ij represents the climb angle, z i，j+1 and z ij are the positions in the z-axis direction of the waypoints. The specific expression of the smooth cost F4 is: where F4(X i ) represents a smooth cost function value, represents a turn angle, a1 represents a weight of the turn angle, ψ ij represents a climb angle, a2 represents a climb angle weight, ψ i，j-1 represents ψ ij a climb angle of the previous position. Considering multiple influencing factors, a total cost function is constructed, which is the weighted cumulative sum of the cost functions under various constraint conditions, and the specific expression is: Wherein, F(X i ) represents the total cost function value, a k represents the weight of the kth path cost, F k (X i ) represents the kth path cost.

3. The unmanned aerial vehicle three-dimensional path planning research method based on the improved HO algorithm according to claim 1, characterized in that The step 2 represents the path as a series of vectors using a spherical coordinate system and finally maps it to rectangular coordinates, including: The vector is expressed in a spherical coordinate system, including three key parameters: the length of the adjacent path point p ∈ (0, path length), the flight elevation angle and the flight azimuth angle For a flight path Ω i with N nodes, it can be represented as a 3N-dimensional hyperspherical vector: where Ω i represents a set of flight paths, p represents a length of adjacent path points, ψ represents a flight elevation angle, represents a flight azimuth angle. a spherical vector is denoted as u ij and is further defined as a vector in the set of paths Ω i , i.e. To convert this spherical vector into a specific waypoint coordinate P ij = (x ij , y ij , z i j) ∈ X i , it can be mapped by the following equation, which is expressed as: z ij = z i，j-1 + p ij cos ψ ij , (14) where x ij and xi，j-1 represent the position of P ij and P i，j-1 on the x-axis, y ij and y i，j-1 represent the position of P ij and P i，j-1 on the y-axis, z ij and z i，j-1 represent the position of P ij and P i，j-1 on the z-axis, p represents the length of the adjacent path point, and ψ represents the flight elevation angle, and φ represents the flight azimuth angle.

4. The unmanned aerial vehicle three-dimensional path planning research method based on the improved HO algorithm according to claim 1, characterized in that The step 3 of the unmanned aerial vehicle three-dimensional path planning research method based on the improved HO algorithm comprises: Each hippo represents a position in space, and the initial stage randomly generates the positions of the hippo population, which can be expressed by the following formula: X i : x ij = l j + r · (u j - l j ), (15) where X i represents the position of the i-th candidate solution, r is a random number between 0 and 1, and l and u represent the lower and upper bounds of the j-th decision variable, respectively. N represents the population size of the hippo population, and n represents the number of decision variables in the problem. The specific expression of the hippo population matrix is as follows: where X is the hippo population matrix, X i represents the ith candidate hippo position. The whole process of the Hippopotamus Optimization Algorithm (HOA) can be divided into three stages: position updating, defense, and escape. The specific algorithm is described as follows: Stage 1: Position updating stage (exploration stage) The hippo population is composed of several adult female hippos, baby hippos, multiple adult male hippos, and a dominant male hippo (the leader of the group). In the optimization algorithm, the position of the dominant male hippo needs to be updated through iterative calculation to ensure that the cost function reaches a minimum value. Formula (17) describes the position updating mechanism of male hippos in lakes or ponds, simulating a mathematical model of their search for the optimal position in the environment. wherein represents the position of a male hippo, x D represents the position of the leading hippo (the hippo with the lowest cost function value in the current iteration). is a random vector between 0 and 1, is a random number between 0 and 1 (see equation (18)), and I1and I2are integers between 1 and 2 (see equation (17)) and (18)). MG i Refers to the mean of some randomly selected Hippo's that have equal probability of containing the Hippo X under consideration i y1 is a random number between 0 and 1 (see equation (17)). In equation (18), Q1 and Q2 are integer random numbers that can be either 1 or 0. wherein I1 and I2 are integers between 1 and 2, is a random vector between 0 and 1, is a random number between 0 and 1, Q1 and Q2 are integer random numbers, which can be 1 or 0. Position of a female or immature in a group of hippopotamuses The specific expression is: Where the specific expression of R is: Where r6 and r7 are a number between 0 and 1 (see formula (21)), and h1 and h2 are randomly selected values or vectors from the five scenarios in formula (18). The specific expression of the position updating of male and female or immature hippos in the group is: where F i is the cost function value, is the male hippo position, is the female or immature hippo position. Stage 2: Defense stage The hippo population will take action to resist the threat of predators. The specific expression of the position of the predator in space is: where Pd j represents the position of the predator, represents a random vector, the value of each element in the vector is between 0 and 1, and l and u represent the lower bound and the upper bound of the jth decision variable, respectively. The distance between the ith hippo and the predator is: wherein, is the distance between the predator and the hippo, Pd j represents the position of the predator, x ij represents the position of the hippo. By studying the second stage of the Hippo optimization algorithm, it is found that the Hippo takes corresponding defense strategies according to the size of to protect itself from the threat of predators. When is less than F i , it means that the predator has approached very close, at which time the Hippo will quickly adjust the direction and actively move towards the predator to exert pressure to force it to retreat. When the value of is larger, it indicates that the predator or invader is still in a remote position, at which time the Hippo does not need to take immediate action, but remains vigilant and observes the other party's movements, and will not make drastic changes. However, it needs to be noted that when is less than F i , the Hippo directly moving towards the predator may bring unnecessary danger, especially in complex environments, too close to the predator may expose the Hippo to more threats, therefore, the Hippo optimization algorithm is proposed by introducing an escape factor based on the spherical vector coordinates, which can combine the escape factor with the updated path position when calculating the updated position, adjust the movement direction of the Hippo, produce a certain degree of fluctuation in the short term, and avoid falling into a local optimal solution, and finally find a better global solution. The specific expression of the escape factor and the position of the hippo when facing the predator is: wherein, is a random vector that obeys a Levy distribution and is used to simulate the mutation of the position of the hippo when attacked by the predator. In equation (27), f is a uniformly random number between 2 and 4, c is a uniformly random number between 1 and 1.5, d is a uniformly random number between 2 and 3. g is a uniformly random number between -1 and 1. is a random vector of dimension 1 x m. The mathematical model of the Levy motion is given by: where ω and u are random numbers in the interval [0, 1], θ is a constant equal to 1.5, r is shorthand for the gamma function, σ ω may be calculated by equation (29). Where θ is a constant equal to 1.5, and Γ is the abbreviation for the gamma function, The hippo position updated in this stage is represented as: wherein, a new defensive position is sought, a cost function value for the new defensive position. Stage 3: Escape stage (development stage) According to the behavior of hippos escaping from predators, the following model is established: wherein t denotes the current iteration number, and T denotes the maximum iteration number MaxIter. denotes the position of the hippo that is closest to the safe position. a1 is a random vector or number that is randomly chosen from three scenarios a in equation (33), denotes a random vector between 0 and 1, while r 12 and r 13 denotes a random number generated in the range of 0 and 1. In addition, r 12 is a normally distributed random number. This stage simulates the behavior of the hippo population escaping from predators, which helps to enhance the exploration ability in local search but neglects the global search. To compensate for this deficiency, the differential evolution algorithm is introduced based on the original algorithm. The differential evolution algorithm generates new individuals by the difference between three random individuals in the current population. This mechanism can guide the search process to explore more superior regions and avoid falling into local optimal solutions in the early stages. Therefore, after introducing the differential evolution algorithm, the algorithm can effectively explore the solution space in the global range, making it more likely to find potential global optimal solutions. In the improved version, the scaling factor F and the crossover probability CR of the differential evolution are dynamically adjusted with the change of the iteration number, and the specific expressions are as follows: F = 0.9 - 0.7 × (t ÷ T), (34) CR = 0.1 + 0.8 × (t ÷ T), (35) Where F represents the scaling factor, t is the current iteration number, T is the maximum iteration number, and CR represents the crossover probability. The differential evolution expression is: V i = X r1 + F · (X r2 - X r3 ), (36) where V i is the mutated individual, X r1 , X r2 , X r3 is randomly selected from the population, and F is the scaling factor for the differential mutation, usually set in the range [0, 1]. The path points generated by the differential evolution (see equation (37)) are then The new path point is obtained by weighting the path points selected in the escape stage of the Hippopotamus Optimization Algorithm (HOA) (see formula (32)) and adding the results after proportionally regulating them. The formula is as follows: where W DE is 0.4, W LS is 0.6, for each updated population its cost function value is calculated, and if the new cost function value is better, the position of the population is updated, expressed in the formula as: wherein, represents the position selected at this stage, is the cost function value corresponding to this point.

5. The method of claim 1, wherein the method is improved based on a HO algorithm. The step 4 finds a set of optimal solutions through a maximum number of iterations: The optimal position and the target cost function value are obtained in each iteration, and the specific expression is as follows: X ibest = X i , (40) F best = F ibes t(X ibest ), (41) where X ibest represents the best position, F best represents the optimal cost function value. The iteration is terminated, and the global optimal fitness value is obtained, and the optimal solution is saved.

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